# DK15: Extension of Algorithms for D-finite functions

The goal in this project part is to extend existing algorithms for the symbolic treatment of functions defined by linear ordinary differential equations with polynomial coefficients (D-finite functions) to more general classes of functions and to implement those algorithms. In particular we consider (a) closure properties for D-finite functions and algorithms introduced in the holonomic systems approach by Zeilberger (and subsequent work), and (b) certified arbitrary precision evaluation (and related topics such as uniform approximation or factorization) as recently investigated by Mezzarobba et al. (based on work of Chudnovsky & Chudnovsky, van der Hoeven,etc.). As the first more general class we consider DD-finite functions, that is, functions defined by linear ODEs with D-finite coefficients. This project combines both symbolic and numeric aspects.